{"title":"地皮、塔和摩天大楼","authors":"Mark Powell, Arunima Ray","doi":"10.1093/oso/9780198841319.003.0012","DOIUrl":null,"url":null,"abstract":"Gropes, towers, and skyscrapers are carefully defined. These are the objects that the rest of Part II studies and seeks to construct. All three are 4-manifolds with boundary, obtained from stacking thickened surfaces on top of one another. Gropes are constructed from thickened orientable surfaces with positive genus, each stage attached to a symplectic basis of curves for the homology of the previous stage. Towers have an additional type of stage obtained from plumbed thickened discs. A skyscraper is the endpoint compactification of an infinite tower. An introduction to endpoint compactifications is included. The notion of a good group is also defined.","PeriodicalId":272723,"journal":{"name":"The Disc Embedding Theorem","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gropes, Towers, and Skyscrapers\",\"authors\":\"Mark Powell, Arunima Ray\",\"doi\":\"10.1093/oso/9780198841319.003.0012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Gropes, towers, and skyscrapers are carefully defined. These are the objects that the rest of Part II studies and seeks to construct. All three are 4-manifolds with boundary, obtained from stacking thickened surfaces on top of one another. Gropes are constructed from thickened orientable surfaces with positive genus, each stage attached to a symplectic basis of curves for the homology of the previous stage. Towers have an additional type of stage obtained from plumbed thickened discs. A skyscraper is the endpoint compactification of an infinite tower. An introduction to endpoint compactifications is included. The notion of a good group is also defined.\",\"PeriodicalId\":272723,\"journal\":{\"name\":\"The Disc Embedding Theorem\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Disc Embedding Theorem\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/oso/9780198841319.003.0012\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Disc Embedding Theorem","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/oso/9780198841319.003.0012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Gropes, towers, and skyscrapers are carefully defined. These are the objects that the rest of Part II studies and seeks to construct. All three are 4-manifolds with boundary, obtained from stacking thickened surfaces on top of one another. Gropes are constructed from thickened orientable surfaces with positive genus, each stage attached to a symplectic basis of curves for the homology of the previous stage. Towers have an additional type of stage obtained from plumbed thickened discs. A skyscraper is the endpoint compactification of an infinite tower. An introduction to endpoint compactifications is included. The notion of a good group is also defined.